public static bool StateMachine(string expression)
{
// Time: O(n). One pass over the entire string from left to right. Evaluates the state of each character against the previous character's valid state transitions.
// Memory: O(1). A constant amount of memory is used to keep track of valid states and bracket counts.
// Treating null and empty string expressions as true
if (string.IsNullOrEmpty(expression))
{
return(true);
}
var bracketStack = new Stack <char>();
var validStateTransitions = ExpressionStateMachine.GetStateTransitions();
foreach (var currentChar in expression)
{
// Check brackets first for possible early return
if (BracketsInvalid(bracketStack, currentChar))
{
return(false);
}
// Get all possible states for the current character
var currentStates = ExpressionStateMachine.GetStates(currentChar);
// Get the next valid state, if it exists
var nextState = GetNextValidState(validStateTransitions, currentStates);
if (nextState == ExpressionStateMachine.ExpressionStateEnum.Invalid)
{
return(false);
}
// Set the collection of valid state transitions for the current state
validStateTransitions = ExpressionStateMachine.GetStateTransitions(nextState);
}
// Check to see if all brackets have a matching pair before returning true
if (bracketStack.Count != 0)
{
return(false);
}
// Check for the Exit state on return in case the expression ends with an invalid state
return(validStateTransitions.Contains(ExpressionStateMachine.ExpressionStateEnum.Exit));
}
private static bool BracketsInvalid(Stack <char> bracketCount, char bracket)
{
if (ExpressionStateMachine.IsOpeningBracket(bracket))
{
bracketCount.Push(bracket);
}
if (ExpressionStateMachine.IsClosingBracket(bracket))
{
var lastBracket = bracketCount.Pop();
if (bracket == ')' && lastBracket != '(')
{
return(true);
}
if (bracket == '}' && lastBracket != '{')
{
return(true);
}
}
return(false);
}
